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Generalised Entropy Accumulation
Tony Metger1, Omar Fawzi2, David Sutter3
1Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.
Communications in Mathematical Physics
|October 15, 2024
Summary
This study introduces a generalized entropy accumulation theorem (EAT) for sequential processes with updated side information. It provides a lower bound on output min-entropy, enhancing security proofs for cryptographic protocols like randomness expansion and quantum key distribution.
Area of Science:
- Quantum Information Theory
- Cryptography
- Mathematical Physics
Background:
- The standard Entropy Accumulation Theorem (EAT) has limitations due to its restrictive model of side information.
- Existing cryptographic protocols often involve complex sequential processes with evolving side information.
Purpose of the Study:
- To generalize the EAT for sequential processes with updatable side information.
- To establish a lower bound for the min-entropy of outputs conditioned on final side information.
- To broaden the applicability of EAT in cryptographic security proofs.
Main Methods:
- Development of a generalized non-signalling condition for sequential processes.
- Application of a new variant of Uhlmann's theorem.
- Derivation of new chain rules for Rényi divergence and entropy.
Main Results:
- A generalized EAT is proven, bounding the min-entropy of outputs based on individual step von Neumann entropies.
- The generalized EAT accommodates more flexible models of side information compared to the original EAT.
- The theorem is applied to provide the first multi-round security proof for blind randomness expansion and simplify the E91 QKD protocol analysis.
Conclusions:
- The generalized EAT offers a more versatile tool for analyzing quantum cryptographic protocols.
- The new mathematical tools developed may have independent theoretical significance.
- This work facilitates more accessible and broader security proofs in quantum cryptography.
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